Question: The first three terms of an arithmetic sequence are given: $7,1,-5, \ldots$ What is the fourth term in the sequence?
Solution: In any arithmetic sequence, each term is equal to the previous term plus the common difference. Thus, the second term is equal to the first term plus the common difference. In this sequence, the second term, $1$ , is $6$ less than the first term, $7$ Therefore, the common difference is $-6$ The fourth term in the sequence is equal to the third term plus the common difference, or $-5 - 6 = -11$.